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Results tagged with hyperbolic-pde
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user 13650
Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
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Unique continuation for the wave equation
Try $u(x,t) = x_1 t$ with $\Gamma = \{x:\; x_1 = 0\}$.
- 54.2k
3
votes
Accepted
Analytic solution of a system of linear, hyperbolic, first order, partial differential equat...
For simplicity, consider solutions where $ u$ does not depend on $x, y$:
$A u_t + B(t) u = 0$. If $y^T A = 0$, that says $y^T B(t) u = 0$, so $u$ is
restricted to belong to a certain (possibly $t$-d …
- 54.2k
1
vote
First order pde with characteristics
This pde can be solved formally as
$$ u(x,y) = F(y - B(x)) $$
where $B(x)$ is an antiderivative of $1/b(x)$ and $F$ is an arbitrary differentiable function.
Of course at points where $b(x)$ is disco …
- 54.2k